Life Expectancy Analysis
ContextBase, https://contextbase.github.io
All programming by John Akwei, Senior Data Scientist
November 9, 2023
Dataset Summary
The attached dataset contains information on life expectancy and various factors related to health and development for different countries over multiple years. The dataset includes the following columns: Country, Year, Status, Life expectancy, Adult Mortality, Infant deaths, Alcohol, Percentage expenditure, Hepatitis B, Measles, BMI, Under-five deaths, Polio, Total expenditure, Diphtheria, HIV/AIDS, GDP, Population, thinness 1-19 years, thinness 5-9 years, Income composition of resources, and Schooling.
Each row represents a specific country and year, providing data on various indicators. The “Country” column indicates the name of the country, while the “Year” column represents the year for which the data is recorded. The “Status” column categorizes countries as either developing or developed.
The dataset includes essential health-related information such as life expectancy, adult mortality rate, infant deaths, alcohol consumption, percentage expenditure on healthcare, vaccination coverage for Hepatitis B and Diphtheria, prevalence of measles, BMI (Body Mass Index), under-five deaths, and HIV/AIDS prevalence.
Additionally, socio-economic indicators are also included, such as GDP (Gross Domestic Product), population, thinness rates for age groups 1-19 years and 5-9 years, income composition of resources, and schooling.
The dataset covers multiple years, allowing for the analysis of trends and changes in various health and development indicators across different countries. It can be used to explore relationships between these factors and gain insights into the overall health and well-being of different populations.
Data Importation
Descriptive data analysis
## Country Year Status Life.expectancy
## Length:2938 Min. :2000 Length:2938 Min. :36.30
## Class :character 1st Qu.:2004 Class :character 1st Qu.:63.10
## Mode :character Median :2008 Mode :character Median :72.10
## Mean :2008 Mean :69.22
## 3rd Qu.:2012 3rd Qu.:75.70
## Max. :2015 Max. :89.00
## NA's :10
## Adult.Mortality infant.deaths Alcohol percentage.expenditure
## Min. : 1.0 Min. : 0.0 Min. : 0.0100 Min. : 0.000
## 1st Qu.: 74.0 1st Qu.: 0.0 1st Qu.: 0.8775 1st Qu.: 4.685
## Median :144.0 Median : 3.0 Median : 3.7550 Median : 64.913
## Mean :164.8 Mean : 30.3 Mean : 4.6029 Mean : 738.251
## 3rd Qu.:228.0 3rd Qu.: 22.0 3rd Qu.: 7.7025 3rd Qu.: 441.534
## Max. :723.0 Max. :1800.0 Max. :17.8700 Max. :19479.912
## NA's :10 NA's :194
## Hepatitis.B Measles BMI under.five.deaths
## Min. : 1.00 Min. : 0.0 Min. : 1.00 Min. : 0.00
## 1st Qu.:77.00 1st Qu.: 0.0 1st Qu.:19.30 1st Qu.: 0.00
## Median :92.00 Median : 17.0 Median :43.50 Median : 4.00
## Mean :80.94 Mean : 2419.6 Mean :38.32 Mean : 42.04
## 3rd Qu.:97.00 3rd Qu.: 360.2 3rd Qu.:56.20 3rd Qu.: 28.00
## Max. :99.00 Max. :212183.0 Max. :87.30 Max. :2500.00
## NA's :553 NA's :34
## Polio Total.expenditure Diphtheria HIV.AIDS
## Min. : 3.00 Min. : 0.370 Min. : 2.00 Min. : 0.100
## 1st Qu.:78.00 1st Qu.: 4.260 1st Qu.:78.00 1st Qu.: 0.100
## Median :93.00 Median : 5.755 Median :93.00 Median : 0.100
## Mean :82.55 Mean : 5.938 Mean :82.32 Mean : 1.742
## 3rd Qu.:97.00 3rd Qu.: 7.492 3rd Qu.:97.00 3rd Qu.: 0.800
## Max. :99.00 Max. :17.600 Max. :99.00 Max. :50.600
## NA's :19 NA's :226 NA's :19
## GDP Population thinness..1.19.years
## Min. : 1.68 Min. :3.400e+01 Min. : 0.10
## 1st Qu.: 463.94 1st Qu.:1.958e+05 1st Qu.: 1.60
## Median : 1766.95 Median :1.387e+06 Median : 3.30
## Mean : 7483.16 Mean :1.275e+07 Mean : 4.84
## 3rd Qu.: 5910.81 3rd Qu.:7.420e+06 3rd Qu.: 7.20
## Max. :119172.74 Max. :1.294e+09 Max. :27.70
## NA's :448 NA's :652 NA's :34
## thinness.5.9.years Income.composition.of.resources Schooling
## Min. : 0.10 Min. :0.0000 Min. : 0.00
## 1st Qu.: 1.50 1st Qu.:0.4930 1st Qu.:10.10
## Median : 3.30 Median :0.6770 Median :12.30
## Mean : 4.87 Mean :0.6276 Mean :11.99
## 3rd Qu.: 7.20 3rd Qu.:0.7790 3rd Qu.:14.30
## Max. :28.60 Max. :0.9480 Max. :20.70
## NA's :34 NA's :167 NA's :163## Life.expectancy Adult.Mortality infant.deaths Alcohol
## Life.expectancy 1 NA NA NA
## Adult.Mortality NA 1 NA NA
## infant.deaths NA NA 1.00000000 NA
## Alcohol NA NA NA 1
## percentage.expenditure NA NA -0.08561222 NA
## percentage.expenditure
## Life.expectancy NA
## Adult.Mortality NA
## infant.deaths -0.08561222
## Alcohol NA
## percentage.expenditure 1.00000000
## # A tibble: 2 × 2
## Status mean_life_expectancy
## <chr> <dbl>
## 1 Developed 79.2
## 2 Developing 67.1
Visualize the Key Variables
Visualize key variables for Life Expectancy with percentage expenditure, Life Expectancy with Hepatitis B, and Life Expectancy with BMI, e.g. time-series patterns, histograms, pair-wise scatter plots.
Time-series plot: Shows the trend of life expectancy over time using
a line plot.
Histogram: Displays the distribution of life expectancy with Hepatitis B
using bars.
Scatter plot: Illustrates the relationship between life expectancy and
BMI using individual points.
Pair-wise scatter plots: Demonstrates the relationships between life
expectancy and percentage expenditure, Hepatitis B, and BMI using
separate scatter plots.
Choose an initial statistical model
Why is this model relevant?
What aspects of data can this model highlight?
Based on the given dataset of life expectancy data, a relevant initial statistical model could be a multiple linear regression model.
The multiple linear regression model is relevant in this context because it allows us to explore the relationship between life expectancy (the dependent variable) and multiple independent variables simultaneously. In this case, we have various independent variables such as health expenditure, Hepatitis B, BMI, and others that may potentially influence life expectancy.
The model can highlight several aspects of the data:
Impact of independent variables: The multiple linear regression model can quantify the impact of each independent variable on life expectancy. By estimating the coefficients of the independent variables, we can understand the direction and magnitude of their influence on life expectancy. For example, we can determine how changes in health expenditure, Hepatitis B prevalence, or BMI are associated with changes in life expectancy.
Significance of independent variables: The model can provide insights into the statistical significance of the independent variables. By examining the p-values associated with the coefficients, we can determine which independent variables have a significant impact on life expectancy. This can help identify the key factors that are strongly associated with life expectancy.
Overall model fit: The multiple linear regression model can provide an overall measure of how well the independent variables explain the variation in life expectancy. The coefficient of determination (R-squared) can indicate the proportion of the total variation in life expectancy that can be explained by the independent variables. A higher R-squared value suggests a better fit of the model to the data.
Residual analysis: The model allows for residual analysis, which helps assess the model’s assumptions and identify potential outliers or influential data points. By examining the residuals (the differences between the observed and predicted life expectancy values), we can check for patterns or systematic deviations that may indicate issues with the model or data.
Overall, a multiple linear regression model is relevant for this data as it provides a framework to explore the relationship between life expectancy and multiple independent variables. It allows us to quantify the impact of various factors, assess their significance, evaluate the overall model fit, and conduct residual analysis to gain insights into the data and potentially make predictions or draw conclusions about life expectancy based on the independent variables.
Choose a proper estimation strategy to fit your model.
A proper estimation strategy to fit the multiple linear regression model would be the Ordinary Least Squares (OLS) method. OLS is a widely used and well-established technique for estimating the parameters of a linear regression model.
Here’s why OLS is a suitable estimation strategy:
Minimization of residuals: OLS aims to minimize the sum of squared residuals between the observed values and the predicted values obtained from the model. By minimizing the residuals, OLS provides the “best-fitting” line that represents the relationship between the dependent variable (life expectancy) and the independent variables.
Linearity assumption: OLS assumes a linear relationship between the dependent variable and the independent variables. It estimates the coefficients of the linear equation that best fits the data. Given that we are considering a multiple linear regression model, OLS is an appropriate method to estimate the coefficients for each independent variable.
Efficiency and unbiasedness: OLS estimators are efficient and unbiased under the assumption of the classical linear regression model. Efficient means that the OLS estimators have the smallest variance among all linear unbiased estimators. Unbiasedness means that, on average, the OLS estimators provide accurate estimates of the true population parameters.
Statistical properties: OLS estimation allows for hypothesis testing and constructing confidence intervals for the coefficients. It provides t-tests and p-values for assessing the significance of individual independent variables, aiding in the identification of variables that have a statistically significant impact on life expectancy.
Ease of implementation: OLS estimation is relatively straightforward to implement in most statistical software packages, including R. The lm() function in R can be used to fit a multiple linear regression model using the OLS method.
While OLS is a suitable estimation strategy for the initial model, it’s important to note that further considerations may be required based on the specific characteristics of the data, such as potential violations of assumptions (e.g., multicollinearity, heteroscedasticity) or the need for advanced techniques (e.g., robust regression, generalized linear models). However, OLS serves as a reliable starting point for estimating the multiple linear regression model.
##
## Call:
## lm(formula = Life.expectancy ~ percentage.expenditure + Hepatitis.B +
## BMI, data = lm_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.9221 -3.7622 0.7341 3.8842 24.2678
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.695e+01 5.114e-01 111.4 <2e-16 ***
## percentage.expenditure 1.481e-03 8.867e-05 16.7 <2e-16 ***
## Hepatitis.B 6.260e-02 5.592e-03 11.2 <2e-16 ***
## BMI 1.802e-01 7.180e-03 25.1 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.704 on 2359 degrees of freedom
## (575 observations deleted due to missingness)
## Multiple R-squared: 0.3681, Adjusted R-squared: 0.3673
## F-statistic: 458 on 3 and 2359 DF, p-value: < 2.2e-16In this code, we use the lm() function to fit the multiple linear regression model. The formula Life expectancy ~ percentage.expenditure + Hepatitis.B + BMI specifies the relationship between the dependent variable (Life expectancy) and the independent variables (percentage.expenditure, Hepatitis.B, and BMI).
The data argument specifies the dataset containing the variables. Make sure to adjust the column names in the formula to match your dataset if they differ.
After fitting the model, we can obtain the model summary using the summary() function. The model summary provides information such as the estimated coefficients, their standard errors, t-values, p-values, and the coefficient of determination (R-squared), among other statistics.
What is your interpretation of the estimated coefficients? Are the signs of your estimated coefficients as you expected? Did you find any counter-intuitive results?
Based on the provided estimated coefficients from the multiple linear regression model, here is an interpretation of the coefficients:
Intercept: The estimated intercept coefficient is 5.695e+01. This represents the estimated average life expectancy when all the independent variables (percentage.expenditure, Hepatitis.B, and BMI) are zero. However, since these variables are unlikely to be exactly zero in real-world scenarios, the intercept may not have a direct practical interpretation.
percentage.expenditure: The estimated coefficient for percentage.expenditure is 1.481e-03. This suggests that, on average, a one-unit increase in percentage expenditure is associated with an estimated increase of 0.001481 in life expectancy, holding other variables constant. This coefficient indicates a positive relationship between percentage expenditure on health and life expectancy.
Hepatitis.B: The estimated coefficient for Hepatitis.B is 6.260e-02. This implies that, on average, a one-unit increase in the Hepatitis B variable is associated with an estimated increase of 0.0626 in life expectancy, holding other variables constant. This coefficient suggests a positive relationship between Hepatitis B prevalence and life expectancy.
BMI: The estimated coefficient for BMI is 1.802e-01. This indicates that, on average, a one-unit increase in BMI is associated with an estimated increase of 0.1802 in life expectancy, holding other variables constant. This coefficient suggests a positive relationship between BMI and life expectancy.
Regarding the signs of the estimated coefficients, they match the expectations. All the coefficients have positive signs, indicating a positive association between the independent variables (percentage.expenditure, Hepatitis.B, and BMI) and life expectancy. This aligns with the intuitive understanding that higher health expenditure, lower Hepatitis B prevalence, and higher BMI tend to be associated with higher life expectancy.
The estimation results do not show any counter-intuitive or unexpected signs in the coefficients. However, it’s important to note that further analysis and interpretation should consider the context of the data, potential confounding factors, and the assumptions and limitations of the multiple linear regression model.
Model Validation
To validate the performance of a multiple linear regression model, there are several techniques you can employ. Here are a few commonly used methods:
Residual Analysis: Residual analysis involves examining the residuals (the differences between the observed and predicted values) to assess the model’s assumptions and identify potential issues. You can plot the residuals against the predicted values or the independent variables to check for patterns or systematic deviations. Ideally, the residuals should be randomly scattered around zero without any discernible patterns. Any patterns or trends in the residuals may indicate violations of assumptions or the presence of outliers.
R-squared and Adjusted R-squared: R-squared measures the proportion of the total variation in the dependent variable that is explained by the independent variables in the model. A higher R-squared value indicates a better fit of the model to the data. However, R-squared tends to increase with the addition of more independent variables, even if they have little practical significance. Adjusted R-squared adjusts for the number of independent variables and provides a more conservative measure of model fit. Comparing R-squared and Adjusted R-squared values can help assess the model’s explanatory power.
Cross-Validation: Cross-validation is a technique to assess how well the model generalizes to unseen data. You can split your dataset into a training set and a validation set. Fit the model on the training set and evaluate its performance on the validation set using metrics such as mean squared error (MSE) or root mean squared error (RMSE). Cross-validation helps estimate the model’s performance on new data and provides an indication of its ability to make accurate predictions.
Hypothesis Testing: Conduct hypothesis tests on the model coefficients to assess their significance. The p-values associated with the coefficients determine whether they have a statistically significant impact on the dependent variable. A low p-value (typically below a predetermined significance level, e.g., 0.05) suggests a significant relationship between the independent variable and the dependent variable.
Outliers and Influential Observations: Identify outliers or influential observations that may have a disproportionate impact on the model. Outliers can distort the model’s fit and predictions. Diagnostic techniques like Cook’s distance or leverage plots can help identify influential observations that have a large impact on the model’s coefficients.
Remember that validation is an iterative process, and it’s important to consider multiple evaluation techniques to gain a comprehensive understanding of the model’s performance. Additionally, it’s crucial to exercise caution and interpret the results in the context of the data and the specific goals of the analysis.
Limitations
The multiple linear regression model has certain limitations that should be considered:
Linearity assumption: Multiple linear regression assumes a linear relationship between the dependent variable and the independent variables. If the relationship is nonlinear, the model may not capture the true underlying pattern effectively.
Independence assumption: The model assumes that the observations are independent of each other. In real-world scenarios, this assumption may be violated if there is correlation or dependence among the observations, leading to biased and inefficient estimates.
Multicollinearity: Multicollinearity occurs when the independent variables are highly correlated with each other. This can make it challenging to interpret the individual effects of the variables and can lead to unstable coefficient estimates.
Outliers and influential observations: Outliers or influential observations can have a disproportionate impact on the model’s fit and predictions. These data points can distort the estimated coefficients and affect the model’s performance.
Heteroscedasticity: Heteroscedasticity refers to the unequal variance of the residuals across different values of the independent variables. Violations of homoscedasticity assumptions can lead to biased standard errors and incorrect inference.
To address these limitations, you may explore alternative models or techniques, such as:
Nonlinear regression: If there is evidence of a nonlinear relationship between the dependent variable and the independent variables, you can consider nonlinear regression models. These models can capture more complex patterns and allow for more flexible functional forms.
Generalized linear models (GLMs): GLMs extend the multiple linear regression framework to handle dependent variables that follow non-normal distributions or have other specific characteristics. Examples of GLMs include logistic regression for binary outcomes or Poisson regression for count data.
Ridge regression or Lasso regression: These are regularization techniques that can help mitigate issues related to multicollinearity by introducing a penalty term in the regression objective function. Ridge regression adds a squared penalty term, while Lasso regression adds an absolute value penalty term. These techniques can reduce the impact of correlated variables and improve the stability of coefficient estimates.
Robust regression: Robust regression methods, such as Huber regression or robust regression based on M-estimators, are designed to handle outliers and influential observations. These techniques downweight the impact of extreme data points, leading to more robust coefficient estimates.
Time series analysis: If the data exhibit temporal dependencies or trends, time series analysis techniques, such as autoregressive integrated moving average (ARIMA) models or state-space models, may be more appropriate. These models can capture the time-dependent patterns and provide better predictions for future time points.
The choice of alternative models depends on the specific characteristics of the data, the research question, and the assumptions you are willing to make. It’s important to carefully consider the limitations of the multiple linear regression model and select an appropriate modeling approach accordingly.
Table 1
##
## Regression Results
## =============================================================
## Dependent variable:
## ------------------------------
## Life Expectancy
## 2010 2015
## (1) (2)
## -------------------------------------------------------------
## Health Expenditures per Capita 0.002*** 0.013
## (0.0003) (0.022)
##
## Constant 68.496*** 71.586***
## (0.682) (0.604)
##
## -------------------------------------------------------------
## Observations 183 183
## R2 0.165 0.002
## Adjusted R2 0.160 -0.004
## Residual Std. Error (df = 181) 8.527 8.138
## F Statistic (df = 1; 181) 35.642*** 0.351
## =============================================================
## Note: *p<0.05; **p<0.01; ***p<0.001